Using Surrogate Data Analysis to Estimate Tau for Local Linear Approximation of Damped Linear Oscillators

One increasingly common way to study individual level data is through the recording of a series of measurements on an individual over time. Within psychology many variables of interest may tend to fluctuate around some average value, moving back and forth around some equilibrium over time. One way that a series of data with these types of fluctuations may be modeled is using the damped linear oscillator model. This model can capture aspects of a series of measurements such as how quickly a set of data fluctuates between two extremes, or whether the magnitude of the fluctuations are increasing or decreasing over time. Unfortunately due to the small, noisy data sets common to psychology, unbiased estimation of the damped linear oscillator model can be very difficult. Application of the methods that fit this model often require the consultation of an individual experienced with implementing these methods. However, it may be possible to automate these methods using a technique called surrogate data analysis, thereby eliminating the need for an expert and making these methods more widely available to researchers. This project explores the possibility of using surrogate data analysis to automate the fitting of the damped linear oscillator model.